Consider the polynomials f(t) = t + 1 and g(t) = (t + 2)(t + k), where k is an arbitrary constant. For which values of the constant k are the three polynomials f(t), tf(t) and g(t) a basis of P2?

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- Oct 18th 2009, 06:29 PMnoles2188matrix of a linear transformation
Consider the polynomials f(t) = t + 1 and g(t) = (t + 2)(t + k), where k is an arbitrary constant. For which values of the constant k are the three polynomials f(t), tf(t) and g(t) a basis of P2?

- Oct 18th 2009, 06:46 PMBruno J.
This will happen when the matrix of coefficients

is nonsingular. Evaluate its determinant, and find the values of for which it is nonzero.